KINETIC MODELING/MATHEMATICAL ANALYSIS OF PHYSIOLOGICAL & BIOCHEMICAL PROCESSES

通过使用定量体内生理和生化过程 放射性示踪剂的研究需要一个合适的数学模型， 描述代谢途径中生化反应的速率 示踪剂和被示踪分子。有效的数值技术， 动力学模型参数估计准确， 统计检验，以检查数据的显著差异， 还需要不同实验组之间的比率。的 实验室正在进行的建模工作解决了这些相互关联的 数学和统计问题;本年度的进展是 在以下具体领域作出的努力： (1)参数鲁棒最小方差自适应（MVA）方法 估计和统计假设检验， 实验室扩展到包括多变量测试程序。的 MVA方法为感兴趣的参数或检验选择估计量 具有最小可能不确定性的统计量，即 最小可能方差 它是适应性的， 在数据之前没有选择特定的估计量或检验统计量 分析.相反，一大群可能的估计或测试 统计被认为是，该过程通过选择 最适合以下数据集的单个估计量或检验统计量 分析. 与参数方法不同，MVA方法不需要先验知识， 关于统计概率分布的假设 底层人口。 (2)提出了一种新的方法来估计测量中的不确定度。 通过时间序列数据的频谱分析检测的成分。光谱 方法，因为它们不需要先验假设， 动力学模型，而是使用后验来确定数量 描述数据所必需的组件，尤其重要 用于正电子发射断层摄影研究的工具， 空间分辨率不足以获得动力学测量 和结构均匀的组织区域。

Quantification of physiological and biochemical processes in vivo by use of radioactive tracers requires an appropriate mathematical model to describe the rates of the biochemical reactions in the metabolic pathway of the tracer and traced molecules. Efficient numerical techniques to estimate accurately the parameters of the kinetic model and powerful statistical tests to examine the data for significant differences in rates among different experimental groups are also required. The Laboratory's ongoing modeling effort addresses these interrelated mathematical and statistical issues; advances in the current year were made in the following specific areas: (1) A robust minimum variance adaptive (MVA) method for parameter estimation and statistical hypothesis testing developed in the Laboratory was extended to include a multivariate testing procedure. The MVA method selects an estimator for the parameter of interest or a test statistic that possesses the minimum possible uncertainty, i.e. the minimum possible variance. It is adaptive in the sense that the specific estimator or test statistic is not chosen prior to the data analysis. Instead, a large group of possible estimators or test statistics is considered, and the procedure adapts by choosing the single estimator or test statistic that is best for the data set under analysis. Unlike parametric methods, the MVA method requires no prior assumptions about the statistical probability distribution of the underlying population. (2) A new technique was developed to estimate the uncertainty in the components detected by spectral analysis of time series data. Spectral methods, because they do not require the a priori postulation of a kinetic model, but rather are used a posteriori to determine the number of components necessary to describe the data, are particularly important tools for use in studies with positron emission tomography in which the spatial resolution is insufficient to obtain measurements in kinetically and structurally homogeneous tissue regions.